# ELATE: Elastic tensor analysis

Welcome to ELATE, the online tool for analysis of elastic tensors, developed by **Romain Gaillac** and **François-Xavier Coudert** at CNRS / Chimie
ParisTech.

If you use the software in published results (paper, conference, etc.), please cite the corresponding paper (*J. Phys. Condens. Matter*, 2016, 28, 275201) and give the
website URL.

ELATE is open source software. Any queries or comments are welcome at

## Summary of the properties

### Input: stiffness matrix (coefficients in GPa) of Ag2F (Materials Project id mp-1391)

95 43 63 8 0 0 43 95 63 -8 0 0 63 63 190 0 0 0 8 -8 0 18 0 0 0 0 0 0 18 8 0 0 0 0 8 26

### Average properties

Averaging scheme | Bulk modulus | Young's modulus | Shear modulus | Poisson's ratio |
---|---|---|---|---|

Voigt | K_{V} = 79.778 GPa | E_{V} = 71.494 GPa | G_{V} = 26.467 GPa | ν_{V} = 0.35064 |

Reuss | K_{R} = 68.729 GPa | E_{R} = 55.917 GPa | G_{R} = 20.491 GPa | ν_{R} = 0.3644 |

Hill | K_{H} = 74.254 GPa | E_{H} = 63.721 GPa | G_{H} = 23.479 GPa | ν_{H} = 0.35697 |

### Eigenvalues of the stiffness matrix

λ_{1} |
λ_{2} |
λ_{3} |
λ_{4} |
λ_{5} |
λ_{6} |
---|---|---|---|---|---|

13.056 GPa | 14.579 GPa | 30.944 GPa | 55.421 GPa | 71.188 GPa | 256.81 GPa |

### Variations of the elastic moduli

Young's modulus | Linear compressibility | Shear modulus | Poisson's ratio | ||||||
---|---|---|---|---|---|---|---|---|---|

E_{min} | E_{max} |
β_{min} | β_{max} | G_{min} | G_{max} |
ν_{min} | ν_{max} | ||

Value | 36.881 GPa | 132.48 GPa | 0.65638 TPa^{–1} | 6.9467 TPa^{–1} | 13.056 GPa | 35.621 GPa | -0.027212 | 0.85615 | Value |

Anisotropy | 3.592 | 10.5833 | 2.728 | ∞ | Anisotropy | ||||

Axis | 0.7175 0.4142 -0.5601 |
0.0000 0.0000 1.0000 |
0.0000 0.0000 1.0000 |
1.0000 0.0000 0.0000 |
-0.0000 0.5257 -0.8507 |
0.5256 0.3035 0.7948 |
-0.5270 0.3043 0.7935 |
-0.4118 0.2375 0.8798 |
Axis |

-1.0000 -0.0000 -0.0000 |
-0.6883 -0.3974 0.6069 |
-0.5000 -0.8660 0.0000 |
-0.7617 0.4402 -0.4754 |
Second axis |

## Spatial dependence of Young's modulus

Young's modulus in (xy) plane

Young's modulus in (xz) plane

Young's modulus in (yz) plane

## Spatial dependence of linear compressibility

linear compressibility in (xy) plane

linear compressibility in (xz) plane

linear compressibility in (yz) plane

## Spatial dependence of shear modulus

Shear modulus in (xy) plane

Shear modulus in (xz) plane

Shear modulus in (yz) plane

## Spatial dependence of Poisson's ratio

Poisson's ratio in (xy) plane

Poisson's ratio in (xz) plane

Poisson's ratio in (yz) plane